Paul understood that his apostleship came ONLY from Jesus. It was not the result of anything he had done, nor had any man done it for him. (Gal. 1:1)
Grace is the gift of God's favor upon us (Gal. 2:15-16), and in a similar way, it is not the result of anything we have done, nor is it the result of what others might have done for us. I am not justified by what I do (works), but rather by why I do it (faith). Paul admonishes those who are trying to turn this around in Galatians 1:6,7.
The actions might look the same to those who do not understand. One gives out of obligation (works) and one out of a sincere understanding and response to the grace of God (faith). The actions look the same, but from God's perspective they are completely different.
If I try to earn God's favor, I am defeated before I begin. I cannot earn His favor. Anything I get from God is simply what He chooses to give me. That is grace.
So to live by grace is to live in response to His beauty and love. To live in a way that tries to earn God's favor is to nulify God's grace. (Gal. 2:21)